The Quantum Supersymmetric Vector Multiplet and Some Problems in Non-Abelian Supergauge Theory

TL;DR

This paper investigates the quantum properties of the supersymmetric vector multiplet, highlighting discrepancies with existing literature, the necessity of positive mass for consistency, and challenges in defining supersymmetric gauge invariance.

Contribution

It provides a purely quantum construction of the supersymmetric vector multiplet, identifies discrepancies in super-propagator expressions, and discusses the difficulties in imposing supersymmetric gauge invariance.

Findings

Super-propagator expressions differ from literature.

Model is consistent only for positive mass.

Challenges in defining supersymmetric gauge invariance.

Abstract

We consider the supersymmetric vector multiplet in a purely quantum framework. We obtain some discrepancies with respect to the literature in the expression of the super-propagator and we prove that the model is consistent only for positive mass. The gauge structure is constructed purely deductive and leads to the necessity of introducing scalar ghost superfields, in analogy to the usual gauge theories. The construction of a consistent supersymmetric gauge theory based on the vector model depends crucially one the definition of gauge invariance. We find some significant difficulties to impose a supersymmetric gauge invariance condition for the usual expressions from the literature.